Beamforming is a ubiquitous task in array signal processing, such as for radar, sonar, acoustics, astronomy, seismology, communications, and medical imaging. The standard data-independent beamformers include the delay-and-sum approach as well as methods based on various data-independent weight vectors for sidelobe control. The data-dependent Capon beamformer adaptively selects the respective weight vectors to minimize the array output power subject to the linear constraint that the signal of interest (SOI) does not suffer from any distortion (unity gain and no phase shift).
The Capon beamformer has better resolution and better interference rejection capability as compared to the data-independent beamformer, provided that the array steering vector corresponding to the SOI is accurately known. However, in practice the SOI steering vector is assumed, rather than being accurately known. This results in steering vector error. Steering vector error generally occurs because of differences between the assumed SOI arrival angle and the true SOI arrival angle and between the assumed array response and the true array response, such as due to array calibration errors. Whenever the SOI steering vector error becomes significant, the performance of the Capon beamformer can become worse than standard beamformers.
Many approaches have been proposed during the past three decades to improve the robustness of the Capon beamformer. To account for array steering vector errors, additional linear constraints, including point and derivative constraints, can be imposed. However, these constraints are not explicitly related to the uncertainty of the array steering vector. Moreover, for every additional linear constraint imposed, the beamformer loses one degree of freedom (DOF) for interference suppression. It has been shown that these constraints belong to the class of covariance matrix tapering approaches.
Diagonal loading (including its extended versions) has been a popular approach to improve the robustness of the Capon beamformer. The diagonal loading approaches are derived by imposing an additional quadratic constraint either on the Euclidean norm of the weight vector itself, or on its difference from a desired weight vector. Sometimes diagonal loading is also proposed to alleviate various problems of using the array sample co-variance matrix and to better control the peak sidelobe responses. However, for most of these methods, it is not clear how to choose the diagonal loading based on the uncertainty of the array steering vector.
The subspace based adaptive beamforming methods require the knowledge of the noise covariance matrix. Hence they are sensitive to the imprecise knowledge of the noise covariance matrix in addition to the array steering vector error. Making these methods robust against the array steering vector error will not cure their sensitivity to imprecise knowledge of the noise covariance matrix.
Most of the early suggested modified Capon beamforming algorithms are rather ad hoc in that the choice of parameters is not directly related to the uncertainty of the steering vector. Only recently have some Capon beamforming methods with a clear theoretical background been proposed, which, unlike the early methods, make explicit use of an uncertainty set of the array steering vector. However, even Capon methods which make explicit use of an uncertainty set of the array steering vector are computationally inefficient and cannot generally provide accurate power estimates for signals of interest.
An improved Capon beamformer method referred to as a robust Capon beamformer (RCB) is described in copending and commonly assigned U.S. application Ser. No. 10/358,597 entitled “Robust Capon Beam forming” by the same inventors as the current application. U.S. application Ser. No. 10/358,597 is hereby incorporated by reference into the current application in its entirety. The method described therein includes the steps of providing a sensor array including a plurality of sensor elements, wherein an array steering vector corresponding to a signal of interest (SOI) is unknown. The array steering vector is represented by an ellipsoidal uncertainty set. A covariance fitting relation for the array steering vector is bounded with the uncertainty ellipsoid. The matrix fitting relation is solved to provide an estimate of the array steering vector.